Here is a very good answer from Archbishop Daniel Pilarczyk (Archbishop of Cincinnati from 1982 to 2009):

"I suppose most people would answer this question by saying that celibacy means that priests are not allowed to get married. That’s true, of course, but celibacy is much more than a negative rule that priests have to observe.

At it’s center, celibacy is a commitment that candidates for the priesthood are expected to make to complete dedication of their lives to the priestly service of the Lord and His people. The celibacy of the priest announces that there is no higher priority in his life than the service of God for God’s people. If I had to give a definition of celibacy, I would call it radical or total availability for God and God’s people. It is not something that the priest takes on for himself but for the Church. It is a gift in service to relationships.

The reason the celibate does not commit himself to marriage is not because there is something wrong with marriage but because marriage and the sexual relationship that marriage involves are an expression of the total gift of the self to another person, and the celibate has already committed himself elsewhere, that is, to the service of the Lord and the Church. This is another way of saying that celibacy is not primarily about sexuality but about a special, passionate love for God’s people. Its sexual dimension is a conclusion that follows from God’s call to service and the celibate’s response.

Celibacy, then, is not so much an obligation as it is a gift. It is a gift from God to the celibate involving the spiritual and psychological gifts that are necessary for one to lead a life of priestly service that puts every other relationship in second place. It is likewise a gift from the celibate to Christ and the Church, a gift to them of all that he is and has.

It is clear, therefore, that priestly celibacy, like the priesthood itself, makes no sense apart from the service of God and His people. It’s not something that the priest does for himself but for Christ and the Church. It is not so much the exclusion of the r elationship of marriage as it is openness to relationships of a different kind. The priestly celibate is a kind of virtuoso of service, but that service has meaning only in the context of the Christian community.

Now that we have seen what celibacy is, it should be clear what it is not. Celibacy is not the mere absence of marriage, nor, still less, the absence of significant human relationships. It is not consecrated bachelorhood. It is not a practical stratagem by which the Church exercises control over its clergy. It is not a mechanism for getting the most work out of priests. It is not an outdated law that cries to be changed.

Rather, celibacy is a lifelong action statement about how God loves His people and about what God has in store for them. It’s a statement that we all need now as perhaps never before."